MS Plan A: FLOW RECONSTRUCTION FROM SURFACE SENSORS ON A SUBMERGED BODY USING BIOT–SAVART–BASED POD MODES

Maliheh Gholizadeh Sarvandi
Masters Student
Department of Ocean & Resources Engineering
University of Hawai’i at Manoa

**This defense will be held in person (POST 418) and Zoom**
Meeting ID: 838 2462 5775
Passcode: MS
Zoom link: https://hawaii.zoom.us/j/83824625775

The external flow around a submerged body produces pressure and shear-stress distributions on its surface, which can be then used as indicators of the full surrounding flow field. Although sensors fixed to the body can measure surface quantities such as pressure and shear stress, they cannot directly measure the external flow field. However, these surface distributions may be interpreted as an encoding of the surrounding flow. The objective of this thesis is therefore to develop a physics-based foundation for future full flow-field reconstruction from this surface-distribution encoding. To address this challenge, a physics-based framework is developed that integrates the Biot–Savart law with the modal structure of Proper Orthogonal Decomposition (POD).  By expressing the Biot–Savart relation in a matrix-based form, the velocity field induced by vorticity is interpreted as a set of spatial kernels analogous to POD modes. This formulation establishes explicit relationships between body geometry, sensor locations, and the corresponding spatial modes in a simplified two-dimensional configuration.

The framework is applied to a family of two-dimensional submerged bodies parameterized by shape coefficients that produce circular, mildly deformed, strongly deformed, peanut-shaped, and multi-lobed geometries. The results show that body geometry strongly influences the structure of an orthogonality map created to visually indicate which sensor locations correspond to orthogonal spatial kernels. For the circular body, orthogonal sensor locations are governed mainly by angular separation, and the corresponding modes form a regular dipole-like family.  As the geometry becomes more complex, zero-crossing locations shift, additional pairwise orthogonal sensor locations appear, and the spatial modes become increasingly affected by local geometric features such as curvature, neck regions, and repeated lobes.  A domain-sensitivity study further shows that the zero-crossing locations remain nearly stable as the computational domain increases, while the modal self-inner products continue to grow approximately logarithmically, indicating that modal norm values, corresponding to time varying coefficients of each spatial mode, are domain-dependent.

Overall, the results demonstrate that the proposed POD–Biot–Savart framework provides a useful foundation for geometry-informed sensor placement and sparse flow reconstruction.  The study shows that body geometry affects not only where sensors should be placed, but also the spatial structure and diversity of the modes that can be captured.  Although increasing geometric complexity expands the number of candidate pairwise orthogonal locations, the identified locations do not necessarily form a mutually orthogonal sensor set, indicating that final sensor selection should be treated as a collective modal-compatibility problem.